Yannis Pantazis

Adaptive AM–FM Signal Decomposition With Application to Speech Analysis

In this paper, we present an iterative method for the accurate estimation of amplitude and frequency modulations (AM-FM) in time-varying multi-component quasi-periodic signals such as voiced speech. Based on a deterministic plus noise representation of speech initially suggested by Laroche (“HNM: A simple, efficient harmonic plus noise model for speech,” Proc. WASPAA, Oct., 1993, pp. 169-172), and focusing on the deterministic representation, we reveal the properties of the model showing that such a representation is equivalent to a time-varying quasi-harmonic representation of voiced speech. Next, we show how this representation can be used for the estimation of amplitude and frequency modulations and provide the conditions under which such an estimation is valid. Finally, we suggest an adaptive algorithm for nonparametric estimation of AM-FM components in voiced speech. Based on the estimated amplitude and frequency components, a high-resolution time-frequency representation is obtained. The suggested approach was evaluated on synthetic AM-FM signals, while using the estimated AM-FM information, speech signal reconstruction was performed, resulting in a high signal-to-reconstruction error ratio (around 30 dB).

Iterative Estimation of Sinusoidal Signal Parameters

While the problem of estimating the amplitudes of sinusoidal components in signals, given an estimation of their frequencies, is linear and tractable, it is biased due to the unavoidable, in practice, errors in the estimation of frequencies. These errors are of great concern for processing signals with many sinusoidal like components as is the case of speech and audio. In this letter, we suggest using a time-varying sinusoidal representation which is able to iteratively correct frequency estimation errors. Then the corresponding amplitudes are computed through Least Squares. Experiments conducted on synthetic and speech signals show the suggested models effectiveness in correcting frequency estimation errors and robustness in additive noise conditions.

Improving the modeling of the noise part in the harmonic plus noise model of speech

Harmonic + noise model (HNM) is a hybrid model of speech with a harmonic component and a noise component. While the harmonic part describes efficiently the periodicities in speech signals (voiced parts), modeling of the noise part introduces artifacts primarily because of the specific time-domain characteristics of noise in voiced speech. In this paper, we concentrated on the modeling of noise in voiced frames. To model the temporal characteristics of noise, we study three time envelopes in the context of HNM; triangular envelope, Hilbert envelope and energy envelope. Listening tests showed a clear preference for the Energy envelope and Hilbert envelope for male voices and to a lesser extent the same conclusions can be drawn for female voices.

A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the relative entropy rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the relative entropy rate and the corresponding Fisher information matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-Gaussian stationary probability distributions, while in the case of high-dimensionality, histograms are impossible to construct directly. Our proposed methods bypass these challenges relying on the direct Monte Carlo simulation of rigorously derived observables for the relative entropy rate and Fisher information in path space rather than on the stationary probability distribution itself. We demonstrate the capabilities of the proposed methodology by focusing here on two classes of problems: (a) Langevin particle systems with either reversible (gradient) or non-reversible (non-gradient) forcing, highlighting the ability of the method to carry out sensitivity analysis in non-equilibrium systems; and, (b) spatially extended kinetic Monte Carlo models, showing that the method can handle high-dimensional problems.

Parametric sensitivity analysis for biochemical reaction networks based on pathwise information theory

BackgroundStochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space.ResultsWe develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters. The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions. For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as “pathwise”. The pathwise sensitivity analysis method is realized by employing the rigorously-derived Relative Entropy Rate, which is directly computable from the propensity functions. A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantifying parameter sensitivities. The structure of the FIM turns out to be block-diagonal, revealing hidden parameter dependencies and sensitivities in reaction networks.ConclusionsAs a gradient-free method, the proposed sensitivity analysis provides a significant advantage when dealing with complex stochastic systems with a large number of parameters. In addition, the knowledge of the structure of the FIM can allow to efficiently address questions on parameter identifiability, estimation and robustness. The proposed method is tested and validated on three biochemical systems, namely: (a) a protein production/degradation model where explicit solutions are available, permitting a careful assessment of the method, (b) the p53 reaction network where quasi-steady stochastic oscillations of the concentrations are observed, and for which continuum approximations (e.g. mean field, stochastic Langevin, etc.) break down due to persistent oscillations between high and low populations, and (c) an Epidermal Growth Factor Receptor model which is an example of a high-dimensional stochastic reaction network with more than 200 reactions and a corresponding number of parameters.

An extension of the adaptive Quasi-Harmonic Model

In this paper, we present an extension of a recently developed AM-FM decomposition algorithm, which will be referred to as the extended adaptive Quasi-Harmonic Model (eaQHM). It was previously shown that the adaptive Quasi-Harmonic Model (aQHM) [1] is an efficient AM-FM decomposition algorithm with applications in speech analysis. In this paper, we show that a simple extension of the aQHM algorithm to include not only frequency but also amplitude adaptation results in higher performance in terms of Signal-to-Reconstruction-Error Ratio (SRER). To support our hypothesis, eaQHM is tested both on synthetic signals and on a subset of the ARCTIC database of speech. Overall, compared with aQHM, eaQHM improves the SRER by more than 2 dB, on average.

Path-Space Information Bounds for Uncertainty Quantification and Sensitivity Analysis of Stochastic Dynamics

Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or even in the model itself. Furthermore, due to their dynamic nature, we need to assess the impact of these uncertainties on the transient and long-time behavior of the stochastic models and derive corresponding uncertainty bounds for observables of interest. A special class of such challenges is parametric uncertainties in the model and in particular sensitivity analysis along with the corresponding sensitivity bounds for stochastic dynamics. Moreover, sensitivity analysis can be further complicated in models with a high number of parameters that render straightforward approaches, such as gradient methods, impractical. In this paper, we derive uncertainty and sensitivity bounds for path-space observables of stochastic dynamics in terms of new goal-oriented divergences; the latter incorporate both observables and information theory objects such as the relative entropy rate. These bounds are tight, depend on the variance of the particular observable and are computable through Monte Carlo simulation. In the case of sensitivity analysis, the derived sensitivity bounds rely on the path Fisher Information Matrix, hence they depend only on local dynamics and are gradient-free. These features allow for computationally efficient implementation in systems with a high number of parameters, e.g., complex reaction networks and molecular simulations.

Chirp rate estimation of speech based on a time-varying quasi-harmonic model

The speech signal is usually considered as stationary during short analysis time intervals. Though this assumption may be sufficient in some applications, it is not valid for high-resolution speech analysis and in applications such as speech transformation and objective voice function assessment for detection of voice disorders. In speech, there are non stationary components, for instance time-varying amplitudes and frequencies, which may change quickly over short time intervals. In this paper, a previously suggested time-varying quasi-harmonic model is extended in order or to estimate the chirp rate for each sinusoidal component, thus successfully tracking fast variations in frequency and amplitude. The parameters of the model are estimated through linear Least Squares and the model accuracy is evaluated on synthetic chirp signals. Experiments on speech signals indicate that the new model is able to efficiently estimate the signal component chirp rates, providing means to develop more accurate speech models for high-quality speech transformations.

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks

Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in “sloppy” systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the number of the sensitive parameters.

Analysis/synthesis of speech based on an adaptive quasi-harmonic plus noise model

Decomposition of speech into a deterministic part and a stochastic part is a typical modeling. Usually, the deterministic part in voiced speech is modeled as a sum of time-varying sinusoids while the stochastic part is modeled as modulated noise. The estimation of sinusoidal parameters assumes that locally speech is a stationary signal. However, this is not true leading to biased amplitude and phase estimation. In this paper, we develop a scheme for speech analysis and synthesis which is able to deal with locally nonstationary frames. Thus, deterministic part it modeled using an adaptive quasi-harmonic model while stochastic part is modeled as time-modulated and frequency-modulated noise. Results show that the reconstructed signal is almost indistinguishable from the original.